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%I #11 Aug 28 2024 09:36:40
%S 1,1,3,5,13,29,71,165,401,957,2315,5561,13437,32377,78191,188617,
%T 455425,1099137,2653699,6405733,15465165,37334149,90133463,217596445,
%U 525326353,1268238029,3061802411,7391815977,17845434365,43082619953,104010674271,251103812113
%N Eigensequence of triangle A168313.
%C Conjectured convergent of a(n)/a(n-1) = (1+sqrt(2)). E.g.: a(19)/a(18) = 2653699/1099137 = 2.4143478...
%F Equals the eigensequence of triangle A168313 = lim_{n->oo} M^n where M = A168313 shifted down one row and inserting a "1" at top.
%F Equals the left column vector as a sequence.
%o (Python)
%o a = [1]
%o for n in range(30):
%o a.append(2*sum(a[n//2:-1]) + a[-1])
%o print(a) # _Andrey Zabolotskiy_, Aug 28 2024
%Y Cf. A168313, A168315.
%K eigen,nonn
%O 1,3
%A _Gary W. Adamson_, Nov 22 2009
%E Terms a(20) and beyond from _Andrey Zabolotskiy_, Aug 28 2024